We introduce a system PSI for a strict implication operator called Priorean strict implication. The semantics for PSI is based on partial Kripke models without accessibility relations. PSI is proved sound and complete with respect to that semantics, and Prior's system Q and related systems are shown to be fragments of PSI or of a mild extension of it.
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- Bull, R. A., ‘An axiomatization of Prior's modal calculus Q’, Notre Dame Journal of Formal Logic 5:211-214, 1964.Google Scholar
- Correia, F. ‘Adequacy results for some Priorean modal propositional logics’, Notre Dame Journal of Formal Logic 40:236-249, 1999.Google Scholar
- Jaspars, J., and E. Thijsse, ‘Fundamentals of partial modal logic’, in P. Doherty, editor, Partiality, Modality, and Nonmonotonicity, CSLI, Stanford, 111-140, 1996.Google Scholar
- Prior, A. N., Time and Modality, Oxford University Press, 1957.Google Scholar
- Prior, A. N., ‘Notes on a group of new modal systems’, Logique et Analyse 2(6–7): 122-127, 1959.Google Scholar
- Prior, A. N., and K. Fine, Worlds, Times and Selves, Amherst: University of Massachusetts Press, 1977.Google Scholar
- Thijsse, E., ‘Partial propositional and modal logic: the overall theory’, in M. Stockhof and L. Torenvliet, editors, Proceedings of the Seventh Amsterdam Colloquium, Part 2, ITLI, Amsterdam, 555-579, 1990.Google Scholar